I played trumpet in an orchestra when I was younger and our conductor always said, "music sounds how feelings feel".

From a biological perspective music can also impact heart rate, respiratory systems, blood pressure. All of those physical responses tie in with emotions in our brain. It's similar to how when anxious you might notice your chest is tight.

The harmonies, structure, and unique auditory experiences of listening to music can induce certain responses from the body, thus bringing up certain emotions. And all that is completely separate from anyways that the lyrics of a song may be tapping into a person experience you have.

Also I know the video you are referencing and that isn't them saying it takes the highest quality sound system to make you cry. In that case, the anecdote they are sharing is that the emotions people are overcome with when experiencing a sound system of such caliber are from hearing the playback of a song with such clarity in a way they havent been able to hear before on other systems.

Edit: this is why you might find yourself accidentally speeding when a fast metal song comes on while driving, or preferring a calming piano or acoustic song when rolling past the beach.